Math

QuestionConvert 6.19×102 nm36.19 \times 10^{2} \mathrm{~nm}^{3} to mm3\mathrm{mm}^{3} and report the answer with correct significant figures.

Studdy Solution

STEP 1

Assumptions1. The given volume is 6.19×10 nm36.19 \times10^{} \mathrm{~nm}^{3} . We need to convert this volume to mm3\mathrm{mm}^{3}
3. We know that 1 mm=106 nm1 \mathrm{~mm} =10^{6} \mathrm{~nm}

STEP 2

First, we need to convert the volume from nm\mathrm{nm}^{} to mm\mathrm{mm}^{}. We can do this by using the conversion factor 1 mm=106 nm1 \mathrm{~mm} =10^{6} \mathrm{~nm}. Since we are dealing with volume, we need to cube this conversion factor.
1 mm=(106 nm)1 \mathrm{~mm}^{} = (10^{6} \mathrm{~nm})^{}

STEP 3

Calculate the value of (106 nm)3(10^{6} \mathrm{~nm})^{3}.
(106 nm)3=1018 nm3(10^{6} \mathrm{~nm})^{3} =10^{18} \mathrm{~nm}^{3}So, 1 mm3=1018 nm31 \mathrm{~mm}^{3} =10^{18} \mathrm{~nm}^{3}.

STEP 4

Now, we can convert the given volume from nm3\mathrm{nm}^{3} to mm3\mathrm{mm}^{3} using the conversion factor.
Volumemm3=Volumenm3/1018Volume_{mm^{3}} = Volume_{nm^{3}} /10^{18}

STEP 5

Plug in the given volume in nm3\mathrm{nm}^{3} to calculate the volume in mm3\mathrm{mm}^{3}.
Volumemm3=.19×102 nm3/1018Volume_{mm^{3}} =.19 \times10^{2} \mathrm{~nm}^{3} /10^{18}

STEP 6

Calculate the volume in mm3\mathrm{mm}^{3}.
Volumemm3=6.19×102 nm3/1018=6.19×1016 mm3Volume_{mm^{3}} =6.19 \times10^{2} \mathrm{~nm}^{3} /10^{18} =6.19 \times10^{-16} \mathrm{~mm}^{3}The volume is 6.19×1016 mm36.19 \times10^{-16} \mathrm{~mm}^{3}.

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